NLDFT Analysis by SAIEUS program

Interactive software for the analysis of adsorption data using NLDFT models.

SAIEUS program has been mentioned in many scientific publications by Google Scholar

More references can be found in Google.

Version 3.0 is an upgrade from version 2.0. The update includes new 2D-NLDFT models, new functionalities, and further improved appearance of graphics.

The SAIEUS1 program (Solution of Adsorption Integral Equation Using Splines) provides smooth and noise free characteristics of the pore structure of porous materials analyzed by adsorption methods.

SAIEUS calculates the pore size distribution (PSD) of these materials from adsorption isotherms using NLDFT models in conjunction with automatic or user-selected conditions.

Two critical elements are necessary for the evaluation of a meaningful pore size distribution:

  1. A theoretical model (kernel) describing adsorption isotherms as a function of the pore size and pressure.
    The models available with this software were derived for several types of materials using one or two-dimensional non local density functional theory (1D, 2D-NLDFT).
  2. A program that is designed to solve the adsorption integral equation (AIE) for the pore size distribution. Practically, the solution of AIE may be obtained by fitting the model to the experimental data.
    In SAIEUS program meaningful and stable results are obtained by employing a regularization method using non-negativity constraints2 combined with optimally minimizing the second derivative (“roughness”) of the calculated distribution via the L-curve method3.


[1] J. Jagiello, Stable Numerical Solution of the Adsorption Integral Equation Using Splines, Langmuir (1994) 10, 2778-2785.

[2] C. L. Lawson and R. J. Hanson, Solving Least Squares Problems, Prentice-Hall, Englewood Cliffs, NJ, 1974.

[3] C. Hansen and D. P. O’Leary, The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems, Siam J. Sci. Comput. (1993) 14, 1487-1503.

[4] J. Jagiello and J. P. Olivier, 2D-NLDFT Adsorption Models for Carbon Slit-Shaped Pores with Surface Energetical Heterogeneity and Geometrical Corrugation, Carbon (2013) 55, 70-80.

[5] J. Jagiello and J. P. Olivier, Carbon Slit Pore Model Incorporating Surface Energetical Heterogeneity and Geometrical Corrugation, Adsorption (2013) 19, 777-783.

[6] J. Jagiello, C. O. Ania, J. B. Parra, C. Cook, Dual Gas Analysis of Microporous Carbons Using 2D-NLDFT Heterogeneous Surface Model and Combined Adsorption Data of N2 and CO2, Carbon (2015) 91, 330-337.

[7] J. Jagiello and J. P. Olivier, A Simple Two-Dimensional NLDFT Model of Gas Adsorption in Finite Carbon Pores. Application to Pore Structure Analysis, Phys. Chem. C (2009) 113, 19382-19385.

[8] J. Jagiello, C. O. Ania, J. B. Parra, L. Jagiello, J. J. Pis, Using DFT Analysis of Adsorption Data of Multiple Gases Including H2 for the Comprehensive Characterization of Microporous Carbons, Carbon (2007) 45, 1066-1077.

[9] J. Jagiello, M. Jaroniec, 2D-NLDFT Adsorption Models for Porous Oxides with Corrugated Cylindrical Pores, Journal of Colloid and Interface Science (2018) 532, 588-597.

[10] P. Li, Q. Chen, T.C. Wang, N.A. Vermeulen, B.L. Mehdi, A. Dohnalkova, N.D. Browning, D. Shen, R. Anderson, D.A. Gómez-Gualdrón, F.M. Cetin, J. Jagiello, A.M. Asiri, J.F. Stoddart, O.K. Farha, Hierarchically Engineered Mesoporous Metal-Organic Frameworks toward Cell-free Immobilized Enzyme Systems, Chem (2018) 4, 1022-1034.

[11] J. Jagiello, J. Kenvin, A. Celzard, V. Fierro, Enhanced Resolution of Ultra Micropore Size Determination of Biochars and Activated Carbons by Dual Gas Analysis Using N2 and CO2 with 2D-NLDFT Adsorption Models, Carbon (2019) 144, 206-215.

[12] J. Jagiello, J. Kenvin, Consistency of Carbon Nanopore Characteristics Derived from Adsorption of Simple Gases and 2D-NLDFT Models. Advantages of Using Adsorption Isotherms of Oxygen (O2) at 77 K, Journal of Colloid and Interface Science (2019) 542, 151-158.

[13] J. Jagiello, J. Kenvin, J. Olivier, A. Lupini, C. Contescu, Using a New Finite Slit Pore Model for NLDFT Analysis of Carbon Pore Structure, Adsorption Science & Technology (2011) 29, 769-780.

[14] J. Jagiello, J. Kenvin, C.O. Ania, J.B. Parra, A. Celzard, V. Fierro, Exploiting the Adsorption of Simple Gases O2 and H2 with Minimal Quadrupole Moments for the Dual Gas Characterization of Nanoporous Carbons Using 2D-NLDFT Models, Carbon (2020) 160, 164-175.

[15] J. Jagiello, T. Kyotani, H. Nishihara, Development of a Simple NLDFT Model for the Analysis of Adsorption Isotherms on Zeolite Templated Carbon (ZTC), Carbon (2020) 169, 205-213.

[16] J. Kenvin, J. Jagiello, S. Mitchell, J. Perez-Ramirez, Unified Method for the Total Pore Volume and Pore Size Distribution of Hierarchical Zeolites from Argon Adsorption and Mercury Intrusion, Langmuir (2015) 31, 1242-1247.